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Estimating Subjective Probabilities

  • Andersen, Steffen


    (Department of Economics, Copenhagen Business School)

  • Fountain, John
  • Harrison, Glenn W.
  • Rutström, Elisabet E.

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or “calibrating adjustments” to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how one can jointly estimate risk attitudes and subjective probabilities using structural maximum likelihood methods. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory.

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Paper provided by Copenhagen Business School, Department of Economics in its series Working Papers with number 05-2009.

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Length: 68 pages
Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:hhs:cbsnow:2009_005
Contact details of provider: Postal: Department of Economics, Copenhagen Business School, Solbjerg Plads 3 C, 5. sal, DK-2000 Frederiksberg, Denmark
Phone: 38 15 25 75
Fax: 38 15 34 99
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  1. Tanga McDaniel & E. Rutström, 2001. "Decision Making Costs and Problem Solving Performance," Experimental Economics, Springer, vol. 4(2), pages 145-161, October.
  2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
  3. Dufwenberg, Martin & Gneezy, Uri, 2000. "Measuring Beliefs in an Experimental Lost Wallet Game," Games and Economic Behavior, Elsevier, vol. 30(2), pages 163-182, February.
  4. Hey, John D & Orme, Chris, 1994. "Investigating Generalizations of Expected Utility Theory Using Experimental Data," Econometrica, Econometric Society, vol. 62(6), pages 1291-1326, November.
  5. Grether, David M., 1992. "Testing bayes rule and the representativeness heuristic: Some experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 17(1), pages 31-57, January.
  6. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
  7. William N. Evans & W. Kip Viscusi, 1993. "Income Effects and the Value of Health," Journal of Human Resources, University of Wisconsin Press, vol. 28(3), pages 497-518.
  8. Gary Charness & Martin Dufwenberg, 2004. "Promises and Partnership," Levine's Bibliography 122247000000000001, UCLA Department of Economics.
  9. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  10. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2008. "Probabilities in Economic Modelling," Levine's Working Paper Archive 122247000000001976, David K. Levine.
  11. Schotter, A. & Sopher, B., 2001. "Social Learning and Coordination Conventions in Inter-Generational Games: An Experimental Study," Working Papers 01-10, C.V. Starr Center for Applied Economics, New York University.
  12. W. Viscusi & William Evans, 2006. "Behavioral Probabilities," Journal of Risk and Uncertainty, Springer, vol. 32(1), pages 5-15, January.
  13. John Fountain & Glenn Harrison, 2011. "What do prediction markets predict?," Applied Economics Letters, Taylor & Francis Journals, vol. 18(3), pages 267-272.
  14. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
  15. Croson, Rachel T. A., 2000. "Thinking like a game theorist: factors affecting the frequency of equilibrium play," Journal of Economic Behavior & Organization, Elsevier, vol. 41(3), pages 299-314, March.
  16. Glenn W. Harrison & Jimmy Martínez-Correa & J. Todd Swarthout, 2012. "Inducing Risk Neutral Preferences with Binary Lotteries: A Reconsideration," Experimental Economics Center Working Paper Series 2012-02, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
  17. Itzhak Gilboa & Andrew W. Postlewaite & David Schmeidler, 2008. "Probability and Uncertainty in Economic Modeling," Journal of Economic Perspectives, American Economic Association, vol. 22(3), pages 173-88, Summer.
  18. Viscusi, W Kip & Evans, William N, 1990. "Utility Functions That Depend on Health Status: Estimates and Economic Implications," American Economic Review, American Economic Association, vol. 80(3), pages 353-74, June.
  19. Ronald Harstad, 2000. "Dominant Strategy Adoption and Bidders' Experience with Pricing Rules," Experimental Economics, Springer, vol. 3(3), pages 261-280, December.
  20. Karni, Edi, 1999. "Elicitation of Subjective Probabilities When Preferences Are State-Dependent," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 479-86, May.
  21. Miguel A. Costa-Gomes & Georg Weizs�cker, 2008. "Stated Beliefs and Play in Normal-Form Games," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 729-762.
  22. Forsythe, Robert & Forrest Nelson & George R. Neumann & Jack Wright, 1992. "Anatomy of an Experimental Political Stock Market," American Economic Review, American Economic Association, vol. 82(5), pages 1142-61, December.
  23. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-45, July.
  24. Holt, Charles A. & Smith, Angela M., 2009. "An update on Bayesian updating," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 125-134, February.
  25. Terrance Hurley & Jason Shogren, 2005. "An Experimental Comparison of Induced and Elicited Beliefs," Journal of Risk and Uncertainty, Springer, vol. 30(2), pages 169-188, January.
  26. Smith, Vernon L, 1969. "Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn," The Quarterly Journal of Economics, MIT Press, vol. 83(2), pages 324-29, May.
  27. Theo Offerman & Joep Sonnemans & Gijs Van De Kuilen & Peter P. Wakker, 2009. "A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes ," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1461-1489.
  28. Charness, Gary B & Dufwenberg, Martin, 2006. "Promises & Partnership," University of California at Santa Barbara, Economics Working Paper Series qt0127h86v, Department of Economics, UC Santa Barbara.
  29. Ernan Haruvy & Yaron Lahav & Charles N. Noussair, 2007. "Traders' Expectations in Asset Markets: Experimental Evidence," American Economic Review, American Economic Association, vol. 97(5), pages 1901-1920, December.
  30. McKelvey, Richard D & Page, Talbot, 1990. "Public and Private Information: An Experimental Study of Information Pooling," Econometrica, Econometric Society, vol. 58(6), pages 1321-39, November.
  31. Li Hao & Daniel Houser, 2012. "Belief elicitation in the presence of naïve respondents: An experimental study," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 161-180, April.
  32. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2014. "Eliciting subjective probabilities with binary lotteries," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 128-140.
  33. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  34. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  35. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  36. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  37. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probability and Uncertainty in Economic Modeling, Second Version," PIER Working Paper Archive 08-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jan 2008.
  38. Hanson, Robin, 1996. "Correction to McKelvey and Page, "Public and Private Information: An Experimental Study of Information Pooling"," Econometrica, Econometric Society, vol. 64(5), pages 1223-24, September.
  39. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, 03.
  40. W. Kip Viscusi & William N. Evans, 1998. "Estimation Of Revealed Probabilities And Utility Functions For Product Safety Decisions," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 28-33, February.
  41. Charles R. Plott & Kathryn Zeiler, 2005. "The Willingness to Pay–Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations," American Economic Review, American Economic Association, vol. 95(3), pages 530-545, June.
  42. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  43. Glenn W. Harrison & Jimmy Martínez-Correa & J. Todd Swarthout & Eric R. Ulm, 2012. "Scoring Rules for Subjective Probability Distributions," Experimental Economics Center Working Paper Series 2012-18, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Apr 2013.
  44. Jaffray, Jean-Yves & Karni, Edi, 1999. "Elicitation of Subjective Probabilities When the Initial Endowment is Unobservable," Journal of Risk and Uncertainty, Springer, vol. 18(1), pages 5-20, April.
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